As I mentioned in the Series Thread, I was looking at the standings at the close of business yesterday and something struck me upside the head. Because there sit the Texas Rangers, with the best W-L record in the entire American League. They've done this by scoring 554 runs and allowing 555 runs.

Which seems a strange formula for success to be sure.

But we saw something very similar just a few years ago, when the 2012 Baltimore Orioles won 24 more games than they lost (93-69) while scoring just 7 more runs than they allowed. Those Orioles went 29-9 in one-run games; this year's Rangers have gone 26-8 in one-run games.

Not so long ago, in the latest of my many, many, many efforts to untangle the phenomena of close games (obviously I'm still haunted and traumatized by the 2005 Blue Jays), I began stumbling towards a way of establishing a team's expected record in one-run games. The principle that began to arise from the murk suggested that in a team's one-run games, the results of roughly half would reflect the team's quality. The results of the other half would reflect the flip of a coin. After a bit of mucking about, I found a formula that works pretty well for large samples.

In 60% of the team's one-run games, use their expected Winning Percentage, using the Pythagorean formula, based on their runs scored and allowed in non-one run games.In 40% of the team's one-run games, flip a coin. Which should come out at .500, and if we flip the coin often enough I'm pretty sure it will come out at .500....

So - if a team has a Pythagorean W-L expectation of .600 and they play 40 one-run games, we expect them to go something like 22-18 in their one-run games (14-10 plus 8-8). Which is .550 ball, and it's pretty much what you should expect from a .600 team in their one-run games.

This formula actually works for large groups of teams and seasons.

But a single season, with just a few dozen one-run games, is a tiny, tiny sample size and anything can happen. Like with the 2012 Orioles and the 2016 Rangers, teams which appear to have flipped the coin and seen it come up heads every time. In fact, they've come up heads so often, they warp the friggin' formula. The quality of the Texas team suggests that they should play .around 500 ball in 60% of their one-run games. So even if the coin came up heads every single time, it wouldn't be enough to get them to 26-8. The best you could expect, with impossibly great luck, would be about 24-10. This is an extremely weird team, folks. )

Anyway, what I was really wondering about this time is this: exactly how did Texas win those 26 games by a single run? Besides being ridiculously, and quite undeservedly lucky - because it's a fluke, folks.

What were the mechanics of this particular fluke? Were they good at holding close leads? Were they bad at holding big leads? Were they good at late inning come backs? How did they do it?

Let's have a look:

WINS1 - April 4: Held 3-2 lead from 5th2 - April 20: Held 2-1 lead from 6th3 - April 27: Held 3-2 lead from 6th4 - May 2: Scored late. Tied after 7.5 - May 11: Held 6-5 from 6th6 - May 14: Walk off at home in extras. (Blew 5-2 lead in 9th)7 - May 15: Late rally, down 6-3 in 7th.8 - May 20: Allowed late run (ahead 2-0 after 3)9 - May 21: Held 2-1 lead from 3rd10 - June 5: Held 3-2 lead from 5th11 - June 6: Walk off at home. Tied after 7.12 - June 7: Allowed late run (ahead 4-2 after 8)13 - June 11: Won in extras.14 - June 17: Held 1-0 lead from 5th15 - June 18: Late rally, down 3-0 after 7, 3-2 after 816 - June 19: Late rally, down 4-3 after 617 - June 20: Held 4-3 lead from 4th.18 - July 1: Scored in extras on the road. Tied after 7.19 - July 8: Held 6-5 lead from 6th20 - July 24: Held 2-1 lead from 7th21 - July 25: Late rally for walkoff at home, down 6-5 after 7.22 - July 28: Scored late. Tied after 5.23 - July 30: Walkoff at home. Tied after 3.24 - August 6: Allowed late run (ahead 3-1 after 8)25 - August 8: Late rally on road, down 3-1 after 8.26 - August 10: Blew 3-1 lead after 7, rallied from 4-3 in 8th.

LOSSES1 - April 7: Walk off loss on the road. Tied after 8. 2 - April 23: Walk off loss on the road. Tied after 10.3 - May 4: Walk off loss on the road. Tied after 6.4 - June 1: Walk off loss on the road in extras.5 - June 24: Blown lead. Ahead 7-4 after 6786 - June 30: Walk off loss on the road. Tied after 57 - July 3: Couldn't catch up. Down 5-2 after 5, 5-4 after 7.8 - August 3: Down 3-2 after 2.

So the next thing I want to do - and I welcome input here, faithful readers - is to define the types of one-run games. This Texas log provides some possibilities. Maybe something like this will cover the various possibilities

1. Walkoff wins - Texas has 4 of these)2. Late run(s) scored (7th inning and later) - Texas has 9 of these3. Late run(s) allowed (creating a one-run game) - Texas has 3 of these4. One run lead held through final 3+ innings - Texas has 10 of these

And something matching for one-run losses

1. Walkoff losses - Texas has 5 of these2. Late runs allowed (7th inning and later) - Texas has 1 of these3. Late runs scored, creating the one-run game - Texas has 1 of these4. One run deficit through final 3+ innings - Texas has 1 of these

And having devised a formula, and having created categories of one-run results... I think I'm ready to get to grips with the 2016 Blue Jays. And the 2015 Jays. And, heaven help us, the 2005 Jays. And other anomalies that hover into view...

Sometimes there is something to be learned by looking at the extremes, sometimes it's just a case of "someone has to finish first (or last)". Clearly playing in Toronto in the 21st century is the biggest factor to underperforming in 1-run games, of course.

Only weird thing I see in Texas's stats is that the best relievers (by ERA) on the team don't really strike people out much - actually the entire bullpen ranks dead last in K/9, and bottom half by most any metric. Whatever the secret to the Rangers, it's not an amazing bullpen (although the back end for them has been dreadful, worse than Storen this year, making the overall RS/RA a little deceiving, maybe).

On the offensive side, the Rangers have hit better in high leverage situations than other ones. The league hits a little worse on average because of pitchers like Britton and Osuna. Ranger pinch-hitters have been abysmal and so it appears to be contagious clutchiness on the part of the regulars.

Now that I'm rested and refreshed, I just ran through the 2016 Jays schedule. They've gone 13-19 in one-run games, as we're all painfully aware. The types of one-run games are completely different.

Here are the Toronto wins:

1. Walkoffs - 4 (same as Texas)
2. Late Run Scored - 3 (Texas has 9)
3. Late Run Allowed - 6 (Texas has 3)
4. Held a Lead - 0 (Texas has 10)

And the Toronto losses

1. Walkoffs - 6 (Texas has 5)
2. Late Run Allowed - 12 (Texas has 1)
3. Late Run Scored - 0 (Texas has 1)
4. Opp Held a Lead - 1 (Texas has 1)

A few things just leap out at you. There's the 12-1 deficit in one-run losses because the team allowed a late run. (And almost half of Toronto's one-run victories are there because the team allowed a late run, creating the one-run situation.) Texas has 9 one-run victories because they scored a late run, either to break a tie or come from behind, while Toronto has just 3.

But especially this: Texas has 10 one-run victories where they took an early one-run lead and held it through the final three innings. So far, this looks rather unusual. Toronto doesn't have any of those, Toronto's opponents have just 1, Texas' opponents have just 1.

Teams whose real winning percentages exceed their expected winning percentages are often referred to as ‘lucky’, and teams who do the opposite are ‘unlucky’. This is a crutch, and it’s far from statistically rigorous.

The reason it is listed as luck is because no method has ever been found that consistently results in a winning record in one run games or that results in a losing record outside of being the Jays it seems :P

Teams whose real winning percentages exceed their expected winning percentages are often referred to as ‘lucky’, and teams who do the opposite are ‘unlucky’. This is a crutch, and it’s far from statistically rigorous. We should not pretend to be able to extract true talent level from two variables alone, and it’s clear that ‘luck’ strikes far more deeply than in simple runs scored and runs allowed in a season. A team with an expected winning percentage of .500 and an actual record of 77-85 is not ‘really’ an 81-win team, although it is true that deviations from pythagorean win-loss are subject to regression. While pure pythagorean expectancy is probably a better way of gauging a team than actual wins and losses, we have some far more informative tricks up our sleeve (we’ll get to them in good time), and so there’s no reason to assume that we’re getting the whole truth from runs scored and runs allowed alone. The idea of pythagorean ‘luck’ is a quick rule of thumb and nothing more.

Sorry for the late replies. I have been considering this for awhile too and have a couple of ideas. First off, a 1-run game is more likeky to be a low scoring game than other games. For example a game with less than 3 total runs scored will be a 1-run game, whereas a game with 30+ runs scored is unlikely to be decided by 1 run.

Secondly, it seems to me that you could test the degree of luck involved by sorting the runs scored or switching the months around. If that radically changes the number of 1 run wins, then it may suggest luck was involved (ties would be 50-50)